Angular-time evolution and edge-spin dynamics in the Haldane phase of the S=1 bilinear-biquadratic chain

We investigate the angular-time evolution – a parameter-time evolution generated by the entanglement Hamiltonian – for the bipartitioned ground state of the S=1 bilinear-biquadratic chain under the open boundary condition with the up edge spin. Using a matrix-product-state representation of the ground-state wavefunction, we calculate the angular-time spin correlation functions $⟨S_n^{\alpha }(\tau )S_{n^{\mathrm{\prime }}}^{\alpha }(0)⟩$ in the Haldane phase, and extract its dominant oscillation mode attributed to the nearly two-fold-degenerate entanglement spectrum associated with the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ symmetry. We also compute the effective edge-spin dynamics under a uniform magnetic field applied to the system part and numerically verify its correspondence to the dominant angular-time mode by precisely comparing the subsystem-size dependence of their amplitudes.